Why ARMA models needs stationarity

I am trying to find why ARMA models needs stationarity to work, I have simulated some nonstationary processes and the estimated parameters (point estimates) seems to be very similar to the actual ones. So, what are the main problems fitting a nonstationary time series with an ARMA model? Is it poor forecast prediction, biased estimates, prediction intervals ? I guess Inference is a problem, but I am concern in the forecast part mainly.

Thanks in advance